WASHINGTON—President Biden and Democratic allies on Monday worked to iron out the remaining disputes over the coronavirus relief package that they hope to push through the Senate this week, despite left-wing frustrations over the exclusion of a minimum-wage increase.

Senate Democrats, who had tried over the weekend to salvage a more limited wage increase through the tax code, scrapped that backup plan late Sunday. With that off the table, Mr. Biden spoke with a group of Senate Democrats about advancing the rest of the bill, as the party works to pass its agenda with narrow majorities in both chambers.

Some of the Democrats who met virtually with Mr. Biden said the discussion focused on targeting some of the bill’s aid.

“We’re just looking for a targeted bill,” Sen. Joe Manchin (D., W.Va.) said after the meeting, saying he wanted to see the legislation “helping the people that need help the most.” Some Democrats have pressed to shift the current income thresholds for the $1,400 direct checks that many Americans would get under the bill so that fewer upper-middle-class families get money. Sen. Jon Tester (D., Mont.) said some changes would likely be made through amendments but would amount to modest alterations to the bill.

Where the minimum-wage issue goes from here is up in the air. Mr. Biden and Senate Democratic leaders made clear that a gradual increase in the federal pay floor to $15 an hour from the current $7.25, passed as part of the House legislation early Saturday, wouldn’t happen in this bill. That eased tensions with Senate centrists who opposed the $15 wage but put new pressure on progressives to swallow their disappointment and coalesce around the president. One prominent House progressive hedged Monday about whether she would vote for the relief bill without the wage boost when the legislation comes back from the Senate.

This post first appeared on wsj.com

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